Infinite Dimentional Morse Theory

• Main Authors: Lin, Ya-ying, 林雅英
• Other Authors: Wu Jyh-yang
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/93529880384624045923

碩士 === 國立中正大學 === 應用數學研究所 === 86 === Part I.II.: Our goal here is to present a Morse theory for differentiable realvalued functions on Hilbert manifolds. This encompasses both forms of Morse theory in a unified way.Part III.: We find that the relationship between the topology of manifolds and the critical points of inequalities, say Morse Inequalities. In addition the generalization of the Morse theory of geodesic to higher loop spaces (i.e. maps of n-disk into a manifold with fixed boundary conditions) and even more general situations works smoothly in this framework, whereas previous attempts at suchgeneralizations were thwarted by the lack of a good analogue of the approximat-ing compact manifolds of piecewise broken geodesics.